Apparatus and method of measuring gas volume fraction of a fluid flowing within a pipe

ABSTRACT

A clamp on apparatus  10,110  is provided that measures the speed of sound or acoustic disturbances propagating in a fluid or mixture having entrained gas/air to determine the gas volume fraction of the flow  12  propagating through a pipe  14 . The apparatus includes an array of pressure sensors clamped onto the exterior of the pipe and disposed axially along the length of the pipe. The apparatus measures the speed of sound propagating through the fluid to determine the gas volume fraction of the mixture using adaptive array processing techniques to define an acoustic ridge in the k-ω plane. The slope of the acoustic ridge  61  defines the speed of sound propagating through the fluid in the pipe.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 10/762,410, filed on Jan. 21, 2004 that claimed thebenefit of U.S. Provisional Patent Application No. 60/528,802 filed Dec.11, 2003, U.S. Provisional Patent Application No. 60/441,652 filed Jan.22, 2003; U.S. Provisional Patent Application No. 60/441,395 filed Jan.21, 2003; which are all incorporated herein by reference.

TECHNICAL FIELD

This invention relates to an apparatus for measuring a flow havingentrained gas therein, and more particularly to a clamp on apparatusthat measures the speed of sound propagating through the flow todetermine the gas volume fraction of the gas in the process.

BACKGROUND ART

The present invention provides a clamp on apparatus and method ofmeasuring gas volume fraction in a process flow or fluid, such asslurries used in the paper and pulp industries and in other industries.Slurries commonly used in the paper and pulp industry are mostly waterand typically contain between 1% and 10% pulp content by mass.Monitoring the gas volume fraction of a slurry can lead to improvedquality and efficiency of the paper production process.

Processes run in the paper and pulp industry can often, eitherintentionally or unintentionally, entrain gas/air. Typically, thisentrained air results in measurement errors in process monitoringequipment such as volumetric flow measurements and consistency meters.

Industry estimates indicate that entrained air levels of 2-4% arecommon. Since most process flow monitors are unable to distinguishbetween air and liquid, interpreting their output as liquid flow rateswould result in a overestimate of the liquid by the volumetric flow rateof the air present at the measurement location. Similarly, for the voidfraction of the air within the pipe can cause errors in consistencymeasurements.

Thus, providing a method and apparatus for measuring entrained air inpaper and pulp slurries, for example, would provide several benefits.Firstly, it would provide a means to screen the output of processinstrumentation. Secondly, in addition to screening the measurements, anaccurate measurement of the entrained air would provide a means tocorrect the output of volumetric flow meters and consistency meters.Thirdly, monitoring variations in the amount of entrained air in a givenprocess could be indicative of process anomalies, such a worn bushing orcavitating pumps and/or valves.

Multiphase process flow rate is a critical process control parameter forthe paper and pulp industry. Knowing the amounts of liquid, solids andentrained gases flowing in process lines is key to optimizing theoverall the papermaking process. Unfortunately, significant challengesremain in the achieving accurate, reliable, and economical monitoring ofmultiphase flow rates of paper and pulp slurries. Reliability challengesarise due the corrosive and erosive properties of the slurry. Accuracychallenges stem from the multiphase nature of the slurries. Economicalchallenges arise from the need to reduce total lifetime cost of flowmeasurement, considering installation and maintenance costs in additionto the initial cost of the equipment.

Currently, there is an unmet need for multiphase flow measurement in theprocessing industry, such as the paper and pulp industry. Real time flowmeasurement is typical restricted to monitoring the total volumetricflow rate in a process line without providing information on thecomposition of the process mixture. For example, electromagnetic flowmeters are the most widely used flow meters in the paper and pulpindustry, however they provide no indication of presence of entrainedair, with its presence resulting in an over prediction of the volumetricflow of process fluid by the amount of air entrained. Consistency meterprovide a measurement of the percentage of solids within the process,however this technology remains more of an art than a science.Furthermore, although entrained air is known to have a large, oftendeleterious, impact on the paper making process, instrumentation iscurrently not available to provide this measurement on a real timebasis.

In one embodiment of the present invention, the apparatus and methodimproves the determination of consistency of paper and pulp slurries.Consistency refers to the mass fraction of pulp contained in water andpulp slurries used in the paper making process. Consistency measurementsare critical in the optimization of the paper making process. Currently,many companies produce consistency meters employing various technologyto serve the paper and pulp industry. Unfortunately, accurate andreliable measurement of consistency remains an elusive objective.Typically, interpreting the output of a consistency meter in terms ofactual consistency is more of an art than a science.

Of the various types of consistency meters on the market, microwavebased meters may represent the best the solution for many applications.One such microwave-based consistency meter is manufactured by Toshiba.Microwave consistency meters essentially measure speed or velocity themicrowave signal propagates through the medium being measured. Forexample, the speed of the microwave signal through water isapproximately 0.1 time the speed of light in a vacuum (c), through airis approximately 1.0 times the speed of light in a vacuum, and throughfiber (or pulp) is approximately 0.6 times the speed of light in avacuum.

The velocity of the microwave signal propagating through the paper pulpslurry is measure by the conductive effects of the slurry, in accordancewith the following equation:V=c*sqrt(E)

Where V is the velocity of the microwave signal propagating through theslurry, c is the speed of light in a vacuum, and E is the relativeconductivity of the material. Typical values of relative conductivityfor material comprising a paper/pulp slurry, for example, are:Water relative conductivity=80;Air relative conductivity=1; andFiber relative conductivity=3.

These meters typically work well in the absence of entrained air. Withentrained air present, the air displaces water and looks like additionalpulp fiber to the microwave meter. Thus, uncertainty in the amount ofentrained air translates directly into uncertainty in consistency.

SUMMARY OF THE INVENTION

Objects of the present invention include an apparatus having a devicefor determining the speed of sound propagating within a pipe todetermine the gas volume fraction of a process fluid or flow flowingwithin a pipe, which can be clamped on or attached to the exterior wallof the pipe.

According to the present invention, an apparatus for measuring the gasvolume fraction process flow flowing within a pipe is provided. Theapparatus includes at least one sensor for providing a sound measurementsignal indicative of the speed of sound propagating within the pipe. Aprocessor determines the gas volume fraction of the flow, in response tothe sound measurement signal.

According to the present invention, a method of measuring the gas volumefraction process flow flowing within a pipe comprises measuring thespeed of sound propagating within the pipe, and determining the gasvolume fraction of the flow, in response to the measured speed of sound.

The foregoing and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an apparatus having an array ofsensors onto a pipe for measuring the volumetric flow and gas volumefraction of the mixture flowing in the pipe having entrained gas/airtherein, in accordance with the present invention.

FIG. 2 is a block diagram of an embodiment of the apparatus of FIG. 1,in accordance with the present invention.

FIG. 3 is a functional flow diagram of an apparatus embodying thepresent invention that compensates the volumetric flow measurement of avolumetric flow meter, in accordance with the present invention.

FIG. 4 is a block diagram of an apparatus for measuring the speed ofsound propagating through a process flow flowing within a pipe, inaccordance with the present invention.

FIG. 5 is a plot of Mixture Sound Speed as a function of gas volumefraction for a 5% consistency slurry over a range of process pressures,in accordance with the present invention.

FIG. 6 is a plot of Mixture Sound Speed a function of gas volumefraction for pure water and a 5% consistency slurry at 4 atm processpressure, in accordance with the present invention.

FIG. 7 is a plot of Mixture Sound Speed as a function of gas volumefraction for different consistency slurry over a range of processpressures, in accordance with the present invention.

FIG. 8 is a plot of Mixture Sound Speed a function of entrained airvolume fraction for slurry at a process pressure, in accordance with thepresent invention.

FIG. 9 is a K-w plot for acoustic field within 3 inch pipe containing˜2% air by volume entrained in water flowing 240 gpm, in accordance withthe present invention.

FIG. 10 is a cross-sectional view of a piezoelectric film sensor inaccordance with the present invention.

FIG. 11 is a top plan view of a piezoelectric film sensor in accordancewith the present invention.

FIG. 12 is a cross-sectional view of a portion of the piezoelectric filmsensor and clamp, in accordance with the present invention.

FIG. 13 is top plan view of a portion of the multi-band sensor assembly,in accordance with the present invention.

FIG. 14 is a prespective view of an assembled multi-band sensor assemblyof FIG. 13, in accordance with the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring to FIG. 1, an apparatus, generally shown as 10, is provided tomeasure gas volume fraction in liquids and mixtures (e.g. paper and pulpslurries or other solid liquid mixtures) having entrained gas therein(including air). The apparatus 10 in accordance with the presentinvention determines the speed at which sound propagates through thefluid 12 within a pipe 14 to measure entrained gas in liquids and/ormixtures 12. To simplify the explanation of the present invention, theflow 12 propagating through the pipe will be referred to as a mixture orslurry with the understanding that the flow may be a liquid or any othermixture having entrained gas therein.

The following approach may be used with any technique that measures thesound speed of a flow or speed at which sound propagates through theflow 12. However, it is particularly synergistic with flow meters usingsonar-based array processing, such as described in U.S. patentapplication, Ser. No. (Cidra's Docket No. CC-0122A) and U.S. patentapplication, Ser. No. 09/729,994 (Cidra's Docket No. CC-0297), filedDec. 4, 200, now U.S. Pat. No. 6,609,069, which are incorporated hereinby reference. While the sonar-based flow meter using an array of sensorsto measure the speed of sound of an acoustic wave propagating throughthe mixture is shown and described, one will appreciate that any meansfor measuring the speed of sound of the acoustic wave may used todetermine the entrained gas volume fraction of the mixture/fluid.

FIG. 2 is a block diagram 1 of the apparatus 10 of FIG. 1 that includesa device 2 for measuring the speed of sound (SOS) propagating throughthe flow 12 within a pipe 14. A pressure sensor and/or temperaturesensor 3,4 measures the pressure and/or temperature, respective, of themixture 12 flowing through the pipe. In response to the speed of soundsignal 5 and the characteristics 6 of the flow (e.g., pressure andtemperature), an entrained gas processing unit 25 determines the gasvolume fraction (GVF) of the flow 12. The pressure and temperaturesensors enables the apparatus 10 to compensate or determine the gasvolume fraction for dynamic changes in the pressure and temperature ofthe flow 12. Alternatively, the pressure and/or temperature may beestimated rather than actually measured.

A flow chart 13 shown in FIG. 3 illustrates the function of theentrained gas processing unit 25. As shown in FIG. 2, the inputs to theprocessing unit 25 includes the speed of sound (SOS) 5 within themixture 12 in the pipe 14, and the pressure and/or temperature of themixture. The fluid properties of the mixture (e.g., SOS and density) aredetermined knowing the pressure and temperature of the mixture. The gasvolume fraction of the mixture (GVF) is determined using the SOSmeasurement and fluid properties, which will be described in greaterdetail hereinafter.

Other information relating to the gas volume fraction in a fluid and thespeed of sound (or sonic velocity) in the fluid, is described in “FluidMechanics and Measurements in two-phase flow Systems”, Institution ofmechanical engineers, proceedings 1969-1970 Vol. 184 part 3C, Sep.24-25, 1969, Birdcage Walk, Westminster, London S.W. 1, England, whichis incorporated herein by reference.

FIG. 1 illustrates a schematic drawing of one embodiment of the presentinvention. The apparatus 10 includes a sensing device 16 comprising anarray of pressure sensors (or transducers) 18-21 spaced axially alongthe outer surface 22 of a pipe 14, having a process flow propagatingtherein. The pressure sensors measure the unsteady pressures produced byacoustical disturbances within the pipe, which are indicative of the SOSpropagating through the mixture 12. The output signals (P1-PN) of thepressure sensors 18-21 are provided to the processor 24, which processesthe pressure measurement data and determines the speed of sound and gasvolume fraction (GVF).

In an embodiment of the present invention shown in FIG. 1, the apparatus10 has at least pressure sensors 18-21 disposed axially along the pipe14 for measuring the unsteady pressure P1-PN of the mixture 12 flowingtherethrough. The speed of sound propagating through the flow 12 isderived by interpreting the unsteady pressure field within the processpiping 14 using multiple transducers displaced axially over ˜2 diametersin length. The flow measurements can be performed using ported pressuretransducers or clamp-on, strain-based sensors.

The apparatus 10 has the ability to measure the gas volume fraction bydetermining the speed of sound of acoustical disturbances or sound wavespropagating through the flow 12 using the array of pressure sensors18-21. While the apparatus of FIG. 1 shows at least four pressuresensors 18-21, the present invention contemplates an apparatus having anarray of two or more pressure sensors and having as many as sixteen (16)pressure sensors.

Generally, the apparatus 10 measures unsteady pressures created byacoustical disturbances propagating through the flow 12 to determine thespeed of sound (SOS) propagating through the flow. Knowing the pressureand/or temperature of the flow and the speed of sound of the acousticaldisturbances, the processing unit 24 can determine the gas volumefraction of the mixture, as described and shown in FIG. 3.

The apparatus in FIG. 1 also contemplates providing one or more acousticsources 27 to enable the measurement of the speed of sound propagatingthrough the flow for instances of acoustically quiet flow. The acousticsource may be a device the taps or vibrates on the wall of the pipe, forexample. The acoustic sources may be disposed at the input end of outputend of the array of sensors 18-21, or at both ends as shown. One shouldappreciate that in most instances the acoustics sources are notnecessary and the apparatus passively detects the acoustic ridgeprovided in the flow 12. The passive noise includes noise generated bypumps, valves, motors, and the turbulent mixture itself.

The apparatus 10 of the present invention may be configured andprogrammed to measure and process the detected unsteady pressuresP₁(t)-P_(N)(t) created by acoustic waves propagating through the mixtureto determine the SOS through the flow 12 in the pipe 14. One suchapparatus 110 is shown in FIG. 4 that measures the speed of sound (SOS)of one-dimensional sound waves propagating through the mixture todetermine the gas volume fraction of the mixture. It is known that soundpropagates through various mediums at various speeds in such fields asSONAR and RADAR fields. The speed of sound propagating through the pipeand mixture 12 may be determined using a number of known techniques,such as those set forth in U.S. patent application Ser. No. 09/344,094,entitled “Fluid Parameter Measurement in Pipes Using AcousticPressures”, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147; U.S.patent application Ser. No. 09/729,994, filed Dec. 4, 2002, now U.S.Pat. No. 6,609,069; U.S. patent application Ser. No. 09/997,221, filedNov. 28, 2001, now U.S. Pat. No. 6,587,798; and U.S. patent applicationSer. No. 10/007,749, entitled “Fluid Parameter Measurement in PipesUsing Acoustic Pressures”, filed Nov. 7, 2001, each of which areincorporated herein by reference.

In accordance with one embodiment of the present invention, the speed ofsound propagating through the mixture 12 is measured by passivelylistening to the flow with an array of unsteady pressure sensors todetermine the speed at which one-dimensional compression waves propagatethrough the mixture 12 contained within the pipe 14.

As shown in FIG. 4, an apparatus 110 embodying the present invention hasan array of at least three acoustic pressure sensors 115,116,117,located at three locations x₁,s₂,x₃ axially along the pipe 14. One willappreciate that the sensor array may include more than three pressuresensors as depicted by pressure sensor 118 at location x_(N). Thepressure generated by the acoustic waves may be measured throughpressure sensors 115-118. The pressure sensors 15-18 provide pressuretime-varying signals P₁(t),P₂(t),P₃(t),P_(N)(t) on lines 120,121,122,123to a signal processing unit 130 to known Fast Fourier Transform (FFT)logics 126,127,128,129, respectively. The FFT logics 126-129 calculatethe Fourier transform of the time-based input signals P₁(t)-P_(N)(t) andprovide complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω),P_(N)(ω) on lines 132,133,134,135 indicative of thefrequency content of the input signals. Instead of FFT's, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)-P_(N)(t), may be used. For example, the cross-spectraldensity and the power spectral density may be used to form a frequencydomain transfer functions (or frequency response or ratios) discussedhereinafter.

The frequency signals P₁(ω)-P_(N)(ω)) are fed to an array processingunit 138 which provides a signal to line 40 indicative of the speed ofsound of the mixture a_(mix), discussed more hereinafter. The a_(mix)signal is provided to an entrained gas processing unit 142, similar tothe processing unit 25, which converts a_(mix) to a percent compositionof a mixture and provides a gas volume fraction or % Comp signal to line44 indicative thereof (as discussed hereinafter).

The data from the array of sensors 115-118 may be processed in anydomain, including the frequency/spatial domain, the temporal/spatialdomain, the temporal/wave-number domain or the wave-number/frequency(k-ω) domain. As such, any known array processing technique in any ofthese or other related domains may be used if desired, similar to thetechniques used in the fields of SONAR and RADAR.

One such technique of determining the speed of sound propagating throughthe flow 12 is using array processing techniques to define an acousticridge in the k-ω plane as shown in FIG. 9. The slope of the acousticridge is indicative of the speed of sound propagating through theflow12. This technique is similar to that described in U.S. Pat. No.6,587,798 filed Nov. 28, 2001, titled “Method and System for DeterminingThe Speed of Sound in a Fluid Within a Conduit”, which is incorporatedherein by reference. The speed of sound (SOS) is determined by applyingsonar arraying processing techniques to determine the speed at which theone dimensional acoustic waves propagate past the axial array ofunsteady pressure measurements distributed along the pipe 14.

The signal processor 24 performs a Fast Fourier Transform (FFT) of thetime-based pressure signals P₁(t)-P_(N)(t) to convert the pressuresignal into the frequency domain. The power of the frequency-domainpressure signals are then determined and defined in the k-ω plane byusing array processing algorithms (such as Capon and Music algorithms).The acoustic ridge in the k-ω plane, as shown in the k-ω plot of FIG. 9,is then determined. The speed of sound (SOS) is determined by measuringslope of the acoustic ridge. The gas volume fraction is then calculatedor otherwise determined, as described hereinafter.

The flow meter of the present invention uses known array processingtechniques, in particular the Minimum Variance, Distortionless Response(MVDR, or Capon technique), to identify pressure fluctuations, whichconvect with the materials flowing in a conduit and accurately ascertainthe velocity, and thus the flow rate, of said material. These processingtechniques utilize the covariance between multiple sensors 18-21 at aplurality of frequencies to identify signals that behave according to agiven assumed model; in the case of the apparatus 10, a model, whichrepresents pressure variations 20 convecting at a constant speed acrossthe pressure sensors comprising the flow meter monitoring head 12.

To calculate the power in the k-ω plane, as represent by a k-ω plot (seeFIG. 9) of either the pressure signals, the processor 58 determines thewavelength and so the (spatial) wavenumber k, and also the (temporal)frequency and so the angular frequency ω, of various spectral componentsof the acoustic waves created passively or actively within the pipe.There are numerous algorithms available in the public domain to performthe spatial/temporal decomposition of arrays of sensor units 18-21.

In the case of suitable acoustic pressures being present, the power inthe k-ω plane shown in a k-ω plot of FIG. 9 so determined will exhibit astructure that is called an acoustic ridge 61 associated with soundpropagating with the flow and one associated with sound propagatingagainst the flow. The acoustic ridge represents the concentration of thedisturbances that propagate with and against the flow and is amathematical manifestation of the relationship between the spatialvariations and temporal variations described above. Such a plot willindicate a tendency for k-ω pairs to appear more or less along a linewith some slope, the slope indicating the speed of sound traveling inboth directions, as is described in more detail below. The power in thek-ω plane so determined is then provided to a acoustic ridge identifier,which uses one or another feature extraction method to determine thelocation and orientation (slope) of any acoustic ridge present in thek-ω plane. Finally, information including the acoustic ridge orientation(slope) is used by an analyzer to determine the speed of sound.

The array processing unit 23 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

The prior art teaches many algorithms of use in spatially and temporallydecomposing a signal from a phased array of sensors, and the presentinvention is not restricted to any particular algorithm. One particularadaptive array processing algorithm is the Capon method/algorithm. Whilethe Capon method is described as one method, the present inventioncontemplates the use of other adaptive array processing algorithms, suchas MUSIC algorithm. The present invention recognizes that suchtechniques can be used to determine speed of sound propagating throughthe fluid 12.

Also, some or all of the functions within the processor 130 may beimplemented in software (using a microprocessor or computer) and/orfirmware, or may be implemented using analog and/or digital hardware,having sufficient memory, interfaces, and capacity to perform thefunctions described herein.

It is within the scope of the present invention that the pressure sensorspacing may be known or arbitrary and that as few as two sensors arerequired if certain information is known about the acoustic propertiesof the process flow 12. The pressure sensors are spaced sufficientlysuch that the entire length of the array (aperture) is at least asignificant fraction of the measured wavelength of the acoustic wavesbeing measured. The acoustic wavelength is a function of the type orcharacteristics of flow 12.

Based on the above discussion, one may use a short length scale apertureto measure the sound speed. For example, the characteristic acousticlength scale is: λ=c/f; where c is the speed of sound in a mixture, f isfrequency and λ is wavelength.

If Aperture=L and if L/λ is approx. constant.Then Lwater/λwater=Lwater*f/C _(water) ≈L _(GVF) *f/c _(GVF)

Therefore: L_(GVF)=Lwater (C_(GVF)/C_(water)); where GVF is gas volumefraction.

Thus for SOS of water (Cwater=5,000 ft/sec), and SOS of the Gas volumefraction (C GVF=500 ft/sec) and a length aperture of L water=5 ft (whichwe have shown is sufficient to accurately measure the SOS of water), thelength aperture for a gas volume fraction L_(GVF) would be about 0.5feet.

The entrained gas processing unit 25 assumes a nearly isothermalcondition for the flow 12. As such the gas volume fraction or the voidfraction is related to the speed of sound by the following quadraticequation:Ax ² +Bx+C=0

wherein x is the speed of sound, A=1+rg/rl*(K_(eff)/P−1)−K_(eff)/P,B=K_(eff)/P−2+rg/rl; C=1−K_(eff)/rl*a_(meas)ˆ2); Rg=gas density,rl=liquid density, K_(eff)=effective K (modulus of the liquid andpipewall), P=pressure, and a_(meas)=measured speed of sound.

Effectively,Gas Voulume Fraction (GVF)=(−B+sqrt(Bˆ2−4*A*C))/(2*A)

Alternatively, the sound speed of a mixture can be related to volumetricphase fraction (φ_(i)) of the components and the sound speed (a) anddensities (ρ) of the component through the Wood equation.$\frac{1}{\rho_{mix}a_{{mix}_{\infty}}^{2}} = {\sum\limits_{i = 1}^{N}\quad\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}}$where $\rho_{mix} = {\sum\limits_{i = 1}^{N}\quad{\rho_{i}\phi_{i}}}$

One dimensional compression waves propagating within a mixture 12contained within a pipe 14 exert an unsteady internal pressure loadingon the pipe. The degree to which the pipe displaces as a result of theunsteady pressure loading influences the speed of propagation of thecompression wave. The relationship among the infinite domain speed ofsound and density of a mixture; the elastic modulus (E), thickness (t),and radius (R) of a vacuum-backed cylindrical conduit; and the effectivepropagation velocity (a_(eff)) for one dimensional compression is givenby the following expression: $\begin{matrix}{a_{eff} = \frac{1}{\sqrt{{1/a_{{mix}_{\infty}}^{2}} + {\rho_{mix}\frac{2R}{Et}}}}} & \left( {{eq}\quad 1} \right)\end{matrix}$

Note: “vacuum backed” as used herein refers to a situation in which thefluid surrounding the pipe externally has negligible acoustic impedancecompared to that of the mixture internal to the pipe 14. For example,meter containing a typical water and pulp slurry immersed in air atstandard atmospheric conditions satisfies this condition and can beconsidered “vacuum-backed”.

The mixing rule essentially states that the compressibility of a mixture(I/(□a²)) is the volumetrically-weighted average of thecompressibilities of the components. For gas/liquid mixtures 12 atpressure and temperatures typical of paper and pulp industry, thecompressibility of gas phase is orders of magnitudes greater than thatof the liquid. Thus, the compressibility of the gas phase and thedensity of the liquid phase primarily determine mixture sound speed, andas such, it is necessary to have a good estimate of process pressure tointerpret mixture sound speed in terms of volumetric fraction ofentrained gas. The effect of process pressure on the relationshipbetween sound speed and entrained air volume fraction is shown in FIG.5.

Conversely, however, detailed knowledge of the liquid/slurry is notrequired for entrained air measurement. Variations in liquid density andcompressibility with changes in consistency have a negligible effect onmixture sound speed compared to the presence of entrained air. FIG. 6shows the mixture sound speed as a function of entrained air volumefraction for two slurries, one with 0% wood fiber and the other with 5%wood fiber by volume. As shown, the relationship between mixture soundspeed and gas volume fraction is essentially indistinguishable for thetwo slurries. Furthermore, mixture sound speed is shown to an excellentindicator of gas volume fraction, especially for the trace to moderateamounts of entrained air, from 0 to 5% by volume, typically encounteredin the paper and pulp industry.

For paper and pulp slurries, the conditions are such that for slurrieswith non-negligible amounts of entrained gas, say <0.01%, the complianceof standard industrial piping (Schedule 10 or 40 steel pipe) istypically negligible compared to that of the entrained air.

FIGS. 7 and 8 above show the relationship between sound speed andentrained air for slurries 12 with pulp contents representative of therange used in the paper and pulp industry. Referring to FIG. 7, twoslurry consistencies are shown; representing the lower limit, a purewater mixture is considered, and representing the higher end ofconsistencies, a 5% pulp/95% water slurry is considered. Since theeffect of entrained air on the sound speed of the mixture is highlysensitive to the compressibility of the entrained air, the effect of theentrained air is examined at two pressures, one at ambient representingthe lower limit of pressure, and one at 4 atmospheres representing atypical line pressure in a paper process. As shown, the consistency ofthe liquid slurry 12, i.e., the pulp content, has little effect on therelationship between entrained air volume fraction and mixture soundspeed. This indicates that an entrained air measurement could beaccurately performed, within 0.01% or so, with little or no knowledge ofthe consistency of the slurry. The chart does show a strong dependenceon line pressure. Physically, this effect is linked to thecompressibility of the air, and thus, this indicates that reasonableestimates of line pressure and temperature would be required toaccurately interpret mixture sound speed in terms of entrained air gasvolume fraction.

FIG. 7 also shows that for the region of interest, from roughly 1%entrained air to roughly 5% entrained air, mixture sound speeds (amix)are quite low compare to the liquid-only sound speeds. In this example,the sound speed of the pure water and the 5% pulp slurry werecalculated, based on reasonable estimates of the constituent densitiesand compressibilities, to be 1524 m/s and 1541 m/s, respectively. Thesound speed of these mixtures with 1% to 5% entrained air at typicaloperating pressure (latm to 4 atms) are on the order of 100 m/sec. Theimplication of these low sound speed is that the mixture sound speedcould be accurately determined with a array of sensors, ie using themethodology described in aforementioned U.S. patent application Ser. No.10/007,749 (Cidra's Docket No. CC-0066B), with an aperture that issimilar, or identical, to an array of sensors that would be suitable todetermine the convection velocity, using the methodology described inaforementioned U.S. patent application, Ser. No. (Cidra's Docket No.CC-0122A), which is incorporated herein by reference.

For the sound speed measurement, the apparatus 110 utilizes arrayprocessing algorithms. The temporal and spatial frequency content ofsound propagating within the process piping is related through adispersion relationship. $k = \frac{\omega}{a_{mix}}$

As before, k is the wave number, defined as k=2π/λ, ω is the temporalfrequency in rad/sec, and a_(mix) is the speed at which sound propagateswithin the process piping. Unlike disturbances, which convect with theflow, however, sound generally propagates in both directions, with andagainst the mean flow. For these cases, the acoustic power is locatedalong two acoustic ridges, one for the sound traveling with the flow ata speed of a_(mix)+V_(mix) and one for the sound traveling against theflow at a speed of a_(mix)−V_(mix).

FIG. 9 shows a k-ω plot generated for acoustic sound field recorded fromwater flowing at a rate of 240 gpm containing ˜2% entrained air byvolume in a 3 in, schedule 10, stainless steel pipe. The k-ω plot wasconstructed using data from an array of strain-based sensors attached tothe outside of the pipe. Two acoustic ridges are clearly evident. Basedon the slopes of the acoustic ridges, the sound speed for this for thismixture was 330 ft/sec (100 m/s), consistent with that predicted by theWood equation. Note that adding 2% air by volume reduces the sound speedof the bubbly mixture to less than 10% of the sound speed of singlephase water.

In one embodiment of the present invention as shown in FIG. 1, each ofthe pressure sensors 18-21 may include a piezoelectric film sensor tomeasure the unsteady pressures of the mixture 12 using either techniquedescribed hereinbefore.

The piezoelectric film sensors include a piezoelectric material or filmto generate an electrical signal proportional to the degree that thematerial is mechanically deformed or stressed. The piezoelectric sensingelement is typically conformed to allow complete or nearly completecircumferential measurement of induced strain to provide acircumferential-averaged pressure signal. The sensors can be formed fromPVDF films, co-polymer films, or flexible PZT sensors, similar to thatdescribed in “Piezo Film Sensors Technical Manual” provided byMeasurement Specialties, Inc., which is incorporated herein byreference. A piezoelectric film sensor that may be used for the presentinvention is part number 1-1002405-0, LDT4-028K, manufactured byMeasurement Specialties, Inc.

Piezoelectric film (“piezofilm”), like piezoelectric material, is adynamic material that develops an electrical charge proportional to achange in mechanical stress. Consequently, the piezoelectric materialmeasures the strain induced within the pipe 14 due to unsteady pressurevariations (e.g., vortical and/or acoustical) within the process mixture12. Strain within the pipe is transduced to an output voltage or currentby the attached piezoelectric sensor. The piezoelectrical material orfilm may be formed of a polymer, such as polarized fluoropolymer,polyvinylidene fluoride (PVDF). The piezoelectric film sensors aresimilar to that described in U.S. patent application Ser. No. (CiDRADocket No. CC-0676), which is incorporated herein by reference.

FIGS. 10 and 11 illustrate a piezoelectric film sensor (similar to thesensor 18 of FIG. 1), wherein the piezoelectric film 32 is disposedbetween and pair of conductive coatings 34,35, such as silver ink. Thepiezoelectric film 32 and conductive coatings 34,35 are coated onto aprotective sheet 36 (e.g., mylar) with a protective coating 38 disposedon the opposing side of the upper conductive coating. A pair ofconductors 40,42 is attached to a respective conductive coating 34,35.

The thickness of the piezoelectric film 32 may be in the range of 8 umto approximately 110 um. The thickness is dependent on the degree ofsensitivity desired or needed to measure the unsteady pressures withinthe pipe 14. The sensitivity of the sensor 30 increases as the thicknessof the piezoelectric film increases.

The advantages of this technique of clamping the PVDF sensor 30 onto theouter surface of the pipe 14 are the following:

-   -   1. Non-intrusive flow rate measurements    -   2. Low cost    -   3. Measurement technique requires no excitation source. Ambient        flow noise is used as a source.    -   4. Flexible piezoelectric sensors can be mounted in a variety of        configurations to enhance signal detection schemes. These        configurations include a) co-located sensors, b) segmented        sensors with opposing polarity configurations, c) wide sensors        to enhance acoustic signal detection and minimize vortical noise        detection, d) tailored sensor geometries to minimize sensitivity        to tube modes, e) differencing of sensors to eliminate acoustic        noise from vortical signals.    -   5. Higher Operating Temperatures (125 C) (co-polymers)

As shown in FIG. 12, the piezoelectric film sensor 30 is adhered orattached to a strap 72 which is then clamped (or strapped) onto theouter surface of the pipe 14 at each respective axial location, similarto that described in U.S. Provisional Application No. 60/425,436 (CidraDocket No. CC-0538), filed Nov. 12, 2002; and U.S. ProvisionalApplication No. 60/426,724 (Cidra Docket No. CC-0554), which areincorporated herein by reference.

As shown in FIG. 12, the piezoelectric film sensor 30 is attached to theouter surface 73 of the strap in relation to the pipe 14. The conductiveinsulator 36 is attached to the outer surface of the strap by doubleside tape or any other appropriate adhesive. The adhesive is preferablyflexible or compliant but minimizes creep between the strap andpiezoelectric film sensor during the operation of the sensor 30. Thelength of the strap is substantially the same as the circumference ofthe pipe 14. The piezoelectric film sensor may extend over thesubstantial length of the strap or some portion less than the strap. Inthe embodiment shown in FIG. 12, the piezoelectric film sensor 30extends substantially the length of the strap 72 to provide acircumferentially averaged pressure signal to the processing unit 24.

Referring to FIG. 12, an attachment assembly 75 comprising a firstattachment block 76, a second attachment block 77 and a spacer 78disposed therebetween, which are welded together to provide slots 79between each of the attachment blocks and the spacer. The slots receiverespective ends of the strap 72 to secure the ends of the straptogether. One end of the strap 72 and the pair of conductors 40,42 arethreaded through the slot disposed between the first attachment blockand the spacer. The strap 72 and conductors 40,42 are secured to theattachment assembly by a pair of fasteners 80. The other end of thestrap is threaded through the slot disposed between the spacer and thesecond attachment block. The other end of the strap is pull tightlybetween the spacer and the second attachment to draw up and take-up thetension and securely clamp the strap to the pipe 14. A set screw withinthe second attachment block is tighten, which then pierces the other endof the strap to secure it to the attachment assembly. The excess portionof the other end of the strap is then cut off. The piezoelectric filmsensor may then be covered with a copper sheet to provide a groundingshield for EMI or other electrical noise.

While the piezoelectric film sensor 30 was mounted to the outer surfaceof the straps 72, the present invention contemplates the piezoelectricfilm sensor may be mounted to the inner surface of the strap, therebyresulting in the piezoelectric sensor being disposed between the strapand the outer surface of the pipe 14.

The present invention also contemplates that the piezoelectric filmsensors 30 of FIGS. 10 and 11 may be mounted directly onto the outerdiameter of the pipe 14 by epoxy, glue or other adhesive.

FIGS. 13 and 14 show another embodiment of the sensing device 16 (orsensor head) mounted to a pipe 14 having fluid 12 flowing therethrough,similar to that described in U.S. patent application Ser. No.10/795,111, filed on Mar. 4, 2004, which is incorporated herein byreference. The sensor head 16 includes a multi-band sensor assembly 40wrapped and mounted to the outer surface 22 of the pipe 14. Themulti-band sensor assembly 40 of the sensor head 16 includes a strip ofpiezoelectric film 50 attached to each band 44 of a multi-band strap 52.The multi-band strap 52 is formed of a single sheet of metallic material(e.g., stainless steel) by stamping or punching voids into the sheetmaterial. The multi-band strap 58 includes a plurality of bands 44 thatare spaced a predetermined distance apart. In the embodiment shown, thebands are equi-spaced, however, the present invention contemplates thatthe straps may be disposed at different spacings. In one embodiment, thespacing is approximately 40% of the diameter of the pipe 14.

The type of unsteady pressure measurement being made (SOS v. VorticalDisturbances) determines the spacing of the sensors 18-21. Measurementof unsteady vortical pressures prefers the array of sensors to be spacedsuch that the length of the array is less than the coherence length ofthe vortical disturbances which is typically on the order of a pipediameter. Measurement of the acoustic pressures prefers the array ofsensors to be space such that the length of the array of sensors 18-21is as long as a predetermined portion of the wavelength of the measuredacoustic signal (e.g., greater than 20% of the wavelength of theacoustic signal). The desired wavelength of the measured acoustic signalis dependent upon the dispersion of particles in the fluid flow, whichis dependent on the particle size, such as that described in U.S. patentapplication Ser. No. 10/349,716 (CiDRA Docket No. CC-0579), filed Jan.23, 2003 and U.S. patent application Ser. No. 10/376,427 (CiDRA DocketNo. CC-0596), filed Feb. 26, 2003, which are all incorporated byreference.

The multi-band strap 52 also includes a plurality of cross members 62spaced along the length of the bands44 to maintain the spacing betweenthe bands over their lengths. The respective ends of the bands are alsointerconnected by opposing end strips 61. The cross members 62 areformed in the shape of an X, however, the invention contemplates thatthe cross members may be in the form of straight members extendingperpendicular between the bands 44 or diagonal to the bands. Thesediagonal members may be angled in the same direction or differentdirections. The cross members 62 advantageously provide that the sensorsare properly spaced apart and maintained at the proper distance duringthe mounting of the sensor assembly 40 to the outer surface 22 of thepipe 14. The interconnection of the bands 44 also permits all thesensors 18-21 to be mounted to the pipe 14 simultaneously and thusreduces the time of mounting the sensor assembly 16 to the pipe. Theunitary multi-band strap 52 ensures the sensors 18-21 are properlyspace.

The present invention also contemplates the multi-band strap 52 maysimply comprise a single sheet of metallic material without cut outs todefine individual bands 44, however, when mounted to the pipe, the sheetmay not uniformally contact the surface 22 of the pipe.

Referring to FIG. 13, each piezoelectric film 50 is mounted, which willbe described in greater detail hereinafter, along the length of arespective band 44 of the sensor strap 52. The electrodes 70 of eachpiezoelectric film 50 are electrically connected (e.g., soldered) to aflexible circuit board 72 mounted along the length at one end strip 61of the multi-band strap 52. The circuit board 72 is secured to themulti-band strap 52 by a plurality of tabs 76 that are welded orotherwise attached to the multi-band strap. The piezoelectric film 50wraps from below the circuit board 72 to the top of the circuit board,where it is soldered thereto. The electrical runs on the circuit board72 interconnect each piezoelectric film 50 to the electrical cable 66 atlocation 78. The electrical cable 41 interconnects with a pre-amplifierunit adjacent an access window of a cover mounted over the sensorassembly and to the pipe.

The multi-band sensor assembly 40 is wrapped around the pipe 14 and theends are attached to each other by a pair of stiffening rails 46. Thestiffening rails 46 are attached (e.g., welded) to the ends of themulti-band strap 52 of the sensor assembly 40. The rails 46 extend thelength of the end strips 61 of the multi-band strap 52. As shown, theends of the multi-band strap 52 are bend to engage the inner surface ofthe rails 46. The bent ends of the multi-band strap 52 are then weldedto the inner surface of each respective rod 46. While the multi-bandstrap 52 is welded to the rails, other fastening means may be used, suchas bolts and screws.

When mounting or clamping the sensor assembly 40 to the pipe 14, theends of the sensor assembly 40 are secured together by bolts or screws54, or other fasteners, which interconnect the stiffening rods 46. Toinsure proper alignment of the rails 46, one rail may include a guidepin and the other rail a hole for receiving the pin. As best shown inFIG. 9, a spring 56 may be disposed on the bolts to provide constanttension on the rails 46.

While the rails 46 are shown to be one continuous rail, the presentinvention contemplates that each rail may comprise a plurality ofshorter rails disposed at the end of each band 44, effective providing asplit rail. Similar to that described, each of the shorter railsopposing each other are bolted together to secure the sensor assembly 40to the pipe 14. This split rail (i.e., plurality of shorter rails)configuration isolates each band 44 from the others an thus permits eachband 44 to more uniformally engage the pipe 14 with out the stress andinfluence of the clamping of the other bands created by the singleunitary rail 46.

As shown in FIG. 14, the sensor assembly 40 includes a shield 43,dispose around the outside of the multi-band strap 52 to provide agrounding shield. The grounding shield may comprise metallic sheetmaterial, screen or web. In one embodiment, the shield 42 is attached tothe sensor assembly 40 by welding one end of the shield to one end ofmulti-band strap 52. The shield 42 wraps around the sensor assembly 40to the opposing end thereof. The opposing end of the shield 42 includesa pair of through holes or windows for receiving bend tabs, which areintegral to the multi-band strap 52. The bend tabs temporarily supportthe shield in place to enable the attachment of the cable ties 48 aroundthe shield.

In a addition to the metallic grounding shield 46, a sheet of polyimidematerial 86 or other suitable non-conductive material is secured to theinner surface of grounding shield, such as by rivets. The polyimidematerial 86 (e.g., Kapton) provides an electrically insulative barrierbetween the piezoelectric film and the shield 46. Further, the polyimidematerial provides a water barrier for the piezoelectric film 50 shouldany water or moisture pass through the shield 46, particularly shield inthe form of a screen or web.

Alternatively, the shield 46 may be secured, such as by welding to bothends of the multi-band strap 52. This method is particularly suited forshields that are in the form of a web or screen, and therefore flexible.

Referring to FIG. 13, the sensor assembly 40 includes a plurality ofstand-offs 81 disposed at the outer edges of the multi-band strap 51 andbetween each of the bands 44. The stand-offs extend substantially thelength of the bands 44. The stand-offs are formed of a flexiblefoam-like material having a thickness great than the thickness of thepiezoelectric film 50 to ensure the shield 46 and polyimide sheet doesnot contact the piezoelectric film when the sensor assembly 40 isclamped/mounted onto a pipe 14.

Advantageously, the single strap 40 having multiple bands 44, each ofwhich having a PVDF sensor 50 mounted thereon, allows the sensor spacingto be set at the time of manufacture to thereby eliminate thepositioning and measuring at the time of installation. Further, thesingle strap 40 allows more accurate positioning (spacing) of thesensors 18-21 than can be attained in a field installation. The singlestrap 52 also provides a more time efficient installation technique overinstalling individual bands 44.

While six sensors have been shown, one will appreciate that sensorassembly 40 may have any number of PVDF sensors 50, including as few astwo sensors and more than six sensors, such as 8, 16 or more sensors.

Another embodiment of the present invention include a pressure sensorsuch as pipe strain sensors, accelerometers, velocity sensors ordisplacement sensors, discussed hereinafter, that are mounted onto astrap to enable the pressure sensor to be clamped onto the pipe. Thesensors may be removable or permanently attached via known mechanicaltechniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. These certain typesof pressure sensors, it may be desirable for the pipe 12 to exhibit acertain amount of pipe compliance.

Instead of single point pressure sensors 18-21, at the axial locationsalong the pipe 12, two or more pressure sensors may be used around thecircumference of the pipe 12 at each of the axial locations. The signalsfrom the pressure sensors around the circumference at a given axiallocation may be averaged to provide a cross-sectional (or circumference)averaged unsteady acoustic pressure measurement. Other numbers ofacoustic pressure sensors and annular spacing may be used. Averagingmultiple annular pressure sensors reduces noises from disturbances andpipe vibrations and other sources of noise not related to theone-dimensional acoustic pressure waves in the pipe 12, thereby creatinga spatial array of pressure sensors to help characterize theone-dimensional sound field within the pipe 12.

The pressure sensors 18-21 of FIG. 1 described herein may be any type ofpressure sensor, capable of measuring the unsteady (or ac or dynamic)pressures within a pipe 14, such as piezoelectric, optical, capacitive,resistive (e.g., Wheatstone bridge), accelerometers (or geophones),velocity measuring devices, displacement measuring devices, etc. Ifoptical pressure sensors are used, the sensors 18-21 may be Bragggrating based pressure sensors, such as that described in U.S. patentapplication, Ser. No. 08/925,598, entitled “High Sensitivity Fiber OpticPressure Sensor For Use In Harsh Environments”, filed Sep. 8, 1997, nowU.S. Pat. No. 6,016,702, and in U.S. patent application, Ser. No.10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensor forMeasuring Unsteady Pressures within a Pipe”, which are incorporatedherein by reference. In an embodiment of the present invention thatutilizes fiber optics as the pressure sensors 14 they may be connectedindividually or may be multiplexed along one or more optical fibersusing wavelength division multiplexing (WDM), time division multiplexing(TDM), or any other optical multiplexing techniques.

In certain embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensors15-18 and it may measure the unsteady (or dynamic or ac) pressurevariations inside the tube 14 by measuring the pressure levels inside ofthe tube. These sensors may be ported within the pipe to make directcontact with the mixture 12. In an embodiment of the present invention,the sensors 14 comprise pressure sensors manufactured by PCBPiezotronics. In one pressure sensor there are integrated circuitpiezoelectric voltage mode-type sensors that feature built-inmicroelectronic amplifiers, and convert the high-impedance charge into alow-impedance voltage output. Specifically, a Model 106B manufactured byPCB Piezotronics is used which is a high sensitivity, accelerationcompensated integrated circuit piezoelectric quartz pressure sensorsuitable for measuring low pressure acoustic phenomena in hydraulic andpneumatic systems. It has the unique capability to measure smallpressure changes of less than 0.001 psi under high static conditions.The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001psi).

The pressure sensors incorporate a built-in MOSFET microelectronicamplifier to convert the high-impedance charge output into alow-impedance voltage signal. The sensor is powered from aconstant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply. A data acquisition system ofthe present invention may incorporate constant-current power fordirectly powering integrated circuit piezoelectric sensors.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

It is also within the scope of the present invention that any strainsensing technique may be used to measure the variations in strain in thepipe, such as highly sensitive piezoelectric, electronic or electric,strain gages and piezo-resistive strain gages attached to the pipe 12.Other strain gages include resistive foil type gages having a race trackconfiguration similar to that disclosed U.S. patent application Ser. No.09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147, which isincorporated herein by reference. The invention also contemplates straingages being disposed about a predetermined portion of the circumferenceof pipe 12. The axial placement of and separation distance ΔX₁, ΔX₂between the strain sensors are determined as described herein above.

It is also within the scope of the present invention that any otherstrain sensing technique may be used to measure the variations in strainin the tube, such as highly sensitive piezoelectric, electronic orelectric, strain gages attached to or embedded in the tube 14.

While a number of sensor have been described, one will appreciate thatany sensor the measures the speed of sound propagating through the fluidmay be used with the present invention, including ultrasonic sensors.

It should be understood that any of the features, characteristics,alternatives or modifications described regarding a particularembodiment herein may also be applied, used, or incorporated with anyother embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. An apparatus for measuring the gas volume fraction process flowflowing within a pipe, the apparatus comprising: at least two sensorsthat provide a sound measurement signal indicative of sound wavespropagating in the process flow flowing within the pipe, wherein thesensors clamp onto or attach to the outer wall of the pipe; and aprocessor that determines the slope of an acoustic ridge in the k-ωplane, in response to the sound measurement signals, to provide a soundspeed signal indicative of the speed of sound propagating through theprocess flow, and that determines the gas volume fraction of the flow,in response to the sound speed signal.
 2. The apparatus of claim 1,wherein the at least two sensors include at least two pressure strainsensors at different axial locations along the pipe, each of thepressure strain sensors providing a respective strain signal indicativeof an acoustic pressure disturbance within the pipe at a correspondingaxial position.
 3. The apparatus of claim 1, wherein the process flow isone of a liquid having entrained gas, a mixture having entrained gas,and a slurry having entrained gas.
 4. The apparatus of claim 2, whereinthe strain sensors are pressure sensors.
 5. The apparatus of claim 1,wherein the processor determines the gas volume fraction using at leastone of the pressure and temperature of the process flow.
 6. Theapparatus of claim 5, wherein the apparatus further includes at leastone of a pressure sensor and temperature sensor to respective determinethe pressure and temperature of the process flow.
 7. The apparatus ofclaim 1, wherein the sound waves are one dimensional acoustic waves. 8.The apparatus of claim 2, wherein the strain sensors are pressuresensors.
 9. The apparatus of claim 1, wherein the processor determinesthe gas volume fraction using at least one of the pressure andtemperature of the process flow.
 10. The apparatus of claim 9, whereinthe apparatus further includes at least one of a pressure sensor andtemperature sensor to respective determine the pressure and temperatureof the process flow.
 11. The apparatus of claim 1, wherein the soundwaves are one dimensional acoustic waves.
 12. The apparatus of claim 1,wherein the at least two sensors include 3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13, 14, 15, or 16 sensors.
 13. The apparatus of claim 1, furtherincludes an acoustic source for generating souond waves within theprocess flow.
 14. The apparatus of claim 1, wherein the sound wave is apassive noise.
 15. The apparatus of claim 1, wherein the gas volumefraction is determined using the following formula:Gas Voulume Fraction=−B+sqrt(Bˆ2−4*A*C))/(2*A) whereinA=1+rg/rl*(K_(eff)/P−1)−K _(eff)/P, B=K_(eff)/P−2+rg/rl;C=1−K_(eff)/rl*a_(meas)ˆ2; Rg=gas density, rl=liquid density,K_(eff)=effective K (modulus of the liquid and pipewall), P=pressure,and a_(meas)=measured speed of sound.
 16. The apparatus of claim 1,wherein the each of the pressure sensors comprises a strap and apiezoelectric film sensor attached to the strap
 17. The apparatus ofclaim 1, wherein the piezoelectric film sensor is attached to the outersurface of the strap and/or the inner surface of the strap.
 18. Theapparatus of claim 1, further includes a clamping device for attachingthe ends of one of the pressure sensors to clamp the pressure sensoronto the pipe.
 19. The apparatus of claim 1, wherein the pressuresensors are removably clamped to the pipe.
 20. The apparatus of claim 1,wherein the piezoelectric film sensor includes at least one ofpolyvinylchlorine fluoride (PDVF), polymer film and flexible PZT.